text: Rare-earth borides REBCN, REBCN and REBC are homologous, i.e. have a similar crystal structure, to BC. The latter has a structure typical of icosahedron-based borides, as shown in figure 11a. There, B icosahedra form a rhombohedral lattice unit (space group: Rm (No. 166), lattice constants: a = 0.56 nm and c = 1.212 nm) surrounding a C-B-C chain that resides at the center of the lattice unit, and both C atoms bridge the neighboring three icosahedra. This structure is layered: as shown in figure 11b, B icosahedra and bridging carbons form a network plane that spreads parallel to the c-plane and stacks along the c-axis.
  These homologous compounds have two basic structure units – the B icosahedron and the B octahedron. The network plane of BC structure can be periodically replaced by a B octahedron layer so that replacement of
  every third, fourth and fifth layer would correspond to REBCN, REBCN and REBC, respectively. The B octahedron is smaller than the B icosahedron; therefore, rare-earth elements can reside in the space created by the replacement. The stacking sequences of BC, REBCN, REBCN and REBC are shown in figures 12a, b, c and d, respectively. High-resolution transmission electron microscopy (HRTEM) lattice images of the latter three compounds, added to Fig. 12, do confirm the stacking sequence of each compound. The symbols 3T, 12R and 15R in brackets indicate the number of layers necessary to complete the stacking sequence, and T and R refer to trigonal and rhombohedral. Thus, REBCN and REBC have rather large c-lattice constants.
  Because of the small size of the B octahedra, they cannot interconnect. Instead, they bond to the B icosahedra in the neighboring layer, and this decreases bonding strength in the c-plane. Nitrogen atoms strengthen the bonding in the c-plane by bridging three icosahedra, like C atoms in the C-B-C chain. Figure 13 depicts the c-plane network revealing the alternate bridging of the boron icosahedra by N and C atoms. Decreasing the number of the B octahedra diminishes the role of nitrogen because the C-B-C chains start bridging the icosahedra. On the other hand, in MgBN the B octahedron layer and the B icosahedron layer stack alternatively and there is no C-B-C chains; thus only N atoms bridge the B icosahedra. However, REBN compounds have not been identified yet.
  Sc, Y, Ho, Er, Tm and Lu are confirmed to form REBCN-type compounds. Single-crystal structure analysis yielded trigonal symmetry for ScBCN (space group Pm1 (No.164) with a = 0.5568(2) and c = 1.0756(2) nm), and the deduced atomic coordinates are summarized in table IVa.
  REBCN was synthesized for Y, Ho, Er, Tm and Lu. The crystal structure, solved for a representative compound YBCN, belongs to the trigonal with space group Rm (No.166); it has six formula units in the unit cell and lattice constants a = b = 0.5623(0) nm and c = 4.4785(3) nm. Atomic coordinates of YBCN are summarized in table IVb.
  Y, Ho, Er, Tm and Lu also form REBC which has a trigonal crystal structure with space group Rm
  (No. 166). Lattice constants of the representative compound YBC are a = b = 0.56457(9) nm and c = 5.68873(13) nm and there are six formula units in the unit cell. Structure data of YBC are
  summarized in table IVc.